#help-0
alpine sable
rancid hazel
also don't forget
2sqrt(i) does equal to sqrt(2)+sqrt(2)i
but there is another value
alpine sable
if we calculated with 2sqrt(i) from beginning on.. would a²-b²= 2
rancid hazel
if we calculated with 2sqrt(i) from beginning on.. would a²-b²= 2
no a²-b² would have still been 0
because 0+ 4i=a²-b²+2abi
rancid hazel
re?
alpine sable
turd
rancid hazel
nah
rancid hazel
you just haven't opened your eyes yet
alpine sable
hahahaha!!!
rancid hazel
once you do...
rancid hazel
hahahahah
rancid hazel
hey one more thing
alpine sable
ye
rancid hazel
2sqrt(i) does equal to sqrt(2)+sqrt(2)i
but there is another value
what is the other value?
alpine sable
but not even my solutions got this
youre above it
youre beyond them
we outsmarted them
you outsmarted them
rancid hazel
don't forget the - when working with square roots
alpine sable
bro i hope you encounter joy and success in your life
rancid hazel
i hope you too
alpine sable
in everything you do
TRULY THANK YOU MAN LMFAOOO YOU SAT HERE WITH ME FOR AN HORU
HOUR
I LOVE YOU BRO!!!!!!!!
okj ill calm donw
alpine sable
of course
i couldnt be more grateful
literally
how come youre so kind
literally
rancid hazel
why not
alpine sable
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! bcuz people suck!! its a filthy world we live in..
im being dramatic ofc
but like
rancid hazel
here is one thing i am going to say
alpine sable
i really admire your patience and your helpfulness
rancid hazel
maybe you keep it or forget about it
but 'don't become negative when your only viewpoint of the world is negative too'
maybe being positive changes something
alpine sable
you have no enemies
rancid hazel
yet
rancid hazel
yes
alpine sable
how old are you anyway
alpine sable
young wise man!!!!!!!!!!!
rancid hazel
how old are you?
rancid hazel
ey still young
alpine sable
same level math despite you being 16 how come
alpine sable
great hobby!
no i think this is cool
i like math too i took extra math class
despite struggling lol
as you saw
rancid hazel
despite struggling lol
you can do one thing to help this
alpine sable
praktis
alpine sable
teacher ask
rancid hazel
alright i'm gonna write something long
alpine sable
optimism ?
rancid hazel
please be patient
rancid hazel
if you are confused about what the hell you are doing why we are squaring this weird i number, why are we doing this. If you ever gotten this feeling, pause and just look at everything you have done in mathematics. Like from preschool all the way to university. Like what is a number again, what is square root, why is the root of a quadratic this weird formula. Once it finally clicks, you can be 100% again with your class mates.
and i want you to really think hard about everything
alpine sable
my father studied engineering and he has a big passion for math, he also always wanted me to think about all the fundamentals when solving an equation
seeing it from a bigger picture and stuff
this applies to life in general too hahah
rancid hazel
my father studied engineering and he has a big passion for math, he also always ...
it's very important, if one of the fundementals seems off to you, then the whole building is gonna collapse.
rancid hazel
ey no problem
alpine sable
its refreshing talking to people like you
alpine sable
everyone is so bitter, but maybe thats just projection of my inner bitterness
rancid hazel
everyone is so bitter, but maybe thats just projection of my inner bitterness
you are not bitter to me
alpine sable
people like you = genuine, kind, helpful, optimistic
and curious!!
and passionatee
you have many great qualitiess
rancid hazel
and negative qualities?
rancid hazel
yet...
alpine sable
i feel like you would deal with them
rancid hazel
xd
rancid hazel
autistic?
rancid hazel
i mean i hate autism
rancid hazel
yep
rancid hazel
yeah the eternal disease that i have
rancid hazel
nah it is a good term
rancid hazel
oh it got auto deleted
alpine sable
lol
rancid hazel
neurodivergent ahh
better than stupid, rutard, ...
rancid hazel
isn't autistic an insult?
alpine sable
well urban dictionary would say its an insult
its used to describe hyperactive behaviour sometimes, i used to get called autistic too often
rancid hazel
its used to describe hyperactive behaviour sometimes, i used to get called autis...
now it is adhd
alpine sable
no i mean like when people talk to eachother like not the official meaning
rancid hazel
i can't socialise well, i can't talk well in person.
rancid hazel
why do you call it a disease ?
.
alpine sable
i can't socialise well, i can't talk well in person.
hmm
i see now why you call it a disease, but i dont agree with this definition
alpine sable
is that the only "downside" to it?
rancid hazel
is that the only "downside" to it?
there are others
alpine sable
there are poeple without autism that are bad at socializing
rancid hazel
there are poeple without autism that are bad at socializing
because they don't got confidence in themselves
alpine sable
lot of factors
rancid hazel
lot of factors
true
but a large majority ofautistic people cannot talk/socialise well
alpine sable
i can see that this could lead to isolation
what conditions must be met in order for you to socialize well
alpine sable
or at least "functional"
alpine sable
but i kinda like being alone
that's not weird at all
i have like 1 friend
after school, i probably wont talk to them anymore either
and I'm not neurodivergent or traumatised in any way.. its just my personality :))
rancid hazel
what conditions must be met in order for you to socialize well
i can't talk to multiple people, that just doesn't work for me. i can't handle loud noises during talking, i can't make large periods of eye contact before breaking.
alpine sable
so, speaking to one person at a time in a library!
alpine sable
then why you call it a disease, you can socialize
everyone has their boundaries
these happen to be yours
rancid hazel
then why you call it a disease, you can socialize
with these conditions that are not present everywhere*
alpine sable
maybe a little more than others
rancid hazel
i might have mild autism but you can see it good by severely autistic people
alpine sable
with these conditions that are not present everywhere*
thats true, but catching one person to talk to is easier actually then talking to multiple people. for the noise thing, thats a bit tricky. you probably wouldnt be able to be in crowds.. but like classrooms and rooms in general
well idk where im going with this
but i think ur cool
rancid hazel
xd
rancid hazel
but i think ur cool
ay thanks man,
but like hey do me one favor before i leave
well 2 but eh
alpine sable
ye
rancid hazel
when someone says to you that they are autistic, please don't treat them like small children.
alpine sable
yeess
rancid hazel
and secondly
alpine sable
did i do that with you?
rancid hazel
eh i try to hide my autism as much as possible
rancid hazel
well maybe i did bcuz youre 16
my classmates know that i am autistic
and one of them treated me like a fucking child
rancid hazel
and secondly
if you have any math questions
don't go to me, other people here can help you too : )
rancid hazel
ay don't be negative
alpine sable
🙂
alpine sable
inshallah
alpine sable
you tooo maaaaaaaaaaaaan <33
weary wyvern
do we have a problem here?
lone heartBOT
@alpine sable Has your question been resolved?
tardy tapir
.close
vocal hawk
if I have digits 1,2,3,4. and I want to have a 3 digit number using these digits, such that the number has two common digits, how many possibilities are there?
pallid scarab
!nosols
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
frigid surge
Shoot mb
frigid surge
if I have digits 1,2,3,4. and I want to have a 3 digit number using these digits...
What do you not get
vocal hawk
What do you not get
my first thought is this:
for the first digits, you have four possibilities, for the second, you still have four, for the third, it depens, if you the first two were the same, then you have three possiblities (the other three digits), if the first two were not the same, then you have two possibilities (one of the two)
and I don't know how to continue from here
frigid surge
Give me sec let me see what I did
- Choose the first digit: 4 choices (1, 2, 3, and 4).
- Choose the second digit, must be the same as the first: You have 1 choice since it has to be the same as the first digit.
- Choose third digit, which must be different from the first two: If the first two digits were the same, you have 3 choices (the remaining 3 digits: 1, 3, and 4). If the first two digits were not same, you have 2 choices (the remaining 2 digits: 3 and 4)
Those were my steps
Do u get that?
vocal hawk
Choose the second digit, must be the same as the first
If the first two digits were the same, you [..] If the first two digits were not same
how come the second digits must be the same as the first but when considering the third digit there are two cases?
and why are the reamaining digits 1,3,4 or 3,4?
perhaps I didn't clarify the question
such that the number has two common digits
I mean that the numbers has a repeated digit, not that it has a "2"
frigid surge
Yes I understood I think
vocal hawk
what?
frigid surge
The second digit must be same as first digit because you want a 3-digit number with two common digits. This means the first and second digits must be exactly the same.
When considering the third digit, there are not two cases; there is only one case: it must be different from the first two digits. This makes it so that you have a 3-digit number with two common digits. So, there is only one case for the third digit, which is to choose a digit different from the first two
Took me a second
vocal hawk
This means the first and second digits must be exactly the same.
no? you can have 122
or 121
vocal hawk
yeah it would
vocal hawk
no, it doesn't mention my condition, which is to have exactly two repeated digits
frigid surge
This is a problem of permutations with repetition, where we have to arrange 3 digits out of 4 possible choices, and one of the digits is repeated twice. The formula for permutations with repetition is n^r, where n is the number of choices and r is the number of positions. In this case, n = 4 and r = 3, so we have 4^3 = 64 possible permutations. However, not all of these permutations have two common digits. To find the ones that do, we can use the following method:
- First, we choose one of the 4 digits to be repeated twice. There are 4 ways to do this.
- Next, we choose one of the remaining 3 digits to be the third digit. There are 3 ways to do this.
- Finally, we arrange the three digits in order. There are 3 ways to do this: XXZ, XZX, or ZXX, where X is the repeated digit and Z is the other digit.
This should help I used part of another stack exchange question
dusty ore
lone heartBOT
dusty ore
can anyone help
frank briar
Use cosine rule and pyhtegorean theorem
true mural
anybody know how i can calculate it? i need to compare them
lone heartBOT
anybody know how i can calculate it? i need to compare them
true mural
what???
shadow bay
Number 4
true mural
thats 8c+5c-15
lone heartBOT
Number 4
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
bleak geyser
anybody know how i can calculate it? i need to compare them
!status
lone heartBOT
anybody know how i can calculate it? i need to compare them
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Do u know what imaginary numbers are
true mural
kinda but didnt learn them yet at school
true mural
i dont really know...
bleak geyser
,calc sqrt[3]{-49}
ocean sealBOT
The following error occured while calculating:
Error: Unexpected operator { (char 8)
ocean sealBOT
ahaan
bleak geyser
,w calc \sqrt[3]{-49}
true mural
oh yea i did this too but i wanted some kind of an explanation
bleak geyser
I know how to do the 2nd one but the first one isn’t possible without complex numbers
bleak geyser
oh yea i did this too but i wanted some kind of an explanation
U just simiply and compare
But how do u simplify the 1st one
bleak geyser
Lemme think I’ll respond in 10 mins if I find out
tall pebble
How would i prove the limit statement
lone heartBOT
How would i prove the limit statement
@tall pebble Has your question been resolved?
Available help channel!
dawn quail
lone heartBOT
dawn quail
b = 7? i'm just guessing here.. it's not clear to me where it ends
it's only clear that "7/n" in the denominator multiplies by 2 each interval
fallen verge
Do you remember the summation formula of an integral?
dawn quail
Do you remember the summation formula of an integral?
do you mean (b-a)/n?
fallen verge
The whole thing
dawn quail
The whole thing
i don't remember
fallen verge
Ngl a lot of them suck on google, lemme tex one up
$\int_a^bf(x)dx=\lim_{n\rightarrow\infty}\left(
\sum_{i=1}^n f\left(a+\frac{i(b-a)}{n}\right) \right)\frac{b-a}{n}$
Frick
Oh my god i cannot do tex today huh
ocean sealBOT
GarlicB
fallen verge
Ok sure
Idk why that worked
Sorry that took so long
So first off, what is your b-a?
Or do you want me to explain the formula
lone heartBOT
@dawn quail Has your question been resolved?
dawn quail
So first off, what is your b-a?
sorry was afk,
thanks for taking the time
b is upper limit
a is lower limit
i believe (b-a)/n is like saying change in x (delta) with respect to intervals (n)
fallen verge
Yes, the (b-a)/n corresponds to the dx in the integral
All the other mumbo jumbo refers to how to find the function value to make the rectangles
dawn quail
All the other mumbo jumbo refers to how to find the function value to make the r...
the epsilon interval is always +1, correct?
if it starts at i=1, it goes up like so with each interval: 2, 3, 4, 5 all the way to n
or if it starts with i=0.5, it goes up like so with each interval: 1.5, 2.5, 3.5, 4.5 all the way up to n?
fallen verge
i starts at 1
This is a left rectangle approximation
Right*
I cannot do directions
lone heartBOT
@dawn quail Has your question been resolved?
vital jasper
does d/dx f(a) = 1/x f(a)
lone heartBOT
does d/dx f(a) = 1/x f(a)
wanton umbra
if d is just a variable
vital jasper
is it not a variable
wanton umbra
if you meant d/(dx)f(a)
lone heartBOT
@vital jasper Has your question been resolved?
tacit arch
does d/dx f(a) = 1/x f(a)
derivative of a constant is 0
reef flame
How is x(4-x) a polynomial function
lone heartBOT
How is x(4-x) a polynomial function
reef flame
And how is 3x+2x not a polynomial function
Can someone help me understand how to tell if it's a polynomial function
proven leaf
And how is 3x+2x not a polynomial function
that is a monomial :)
mono + (no)mial = "One number/term" and poly + nomial "many numbers/terms"
3x+2x simplifies to 5x, notice how this has one term
albeit, in reality most people just call it a polynomial 
but pedantics will be pedantics
reef flame
I see
sour dove
mono + (no)mial = "One number/term" and poly + nomial "many numbers/terms"
I like how you explain things
proven leaf
I like how you explain things
thank you! also howdy there mellow! 
reef flame
For x(4-x) how is the leading coefficient -1
Isn't it 1 I saw answer key said -1
@proven leaf
proven leaf
For x(4-x) how is the leading coefficient -1
the leading coefficient is the coefficient on the largest power of x
in the case of x(4-x) that is x^2
it becomes 4x-x^2, and rearranging we get -x^2+4x
so our leading coefficeint is -1 :)
lone heartBOT
lone heartBOT
Available help channel!
lilac solstice
lone heartBOT
lilac solstice
Lim laws don’t apply here because zero is in the denominator or is it because f(x) L doesn’t equal R?
proven leaf
yep that limit law if only true if $\lim_{x\to a}g(x)\neq0$
ocean sealBOT
MrFancy
lilac solstice
Ok so I am a bit confused on the answer also. My professor wrote 0, but I thought it would be DNE because of the denominator issue.
lone heartBOT
@lilac solstice Has your question been resolved?
lilac solstice
.close
tidal cargo
having a hard time understanding how to start this one out
lone heartBOT
having a hard time understanding how to start this one out
dusk umbra
tidal cargo
having a hard time understanding how to start this one out
proven leaf
having a hard time understanding how to start this one out
first what is a parabola with zeroes 7 and 1? 
tidal cargo
a parabola thats x-intercepts are at (7,0) and (1,0) right
proven leaf
so how would you write out an equation for such a parabola?
tidal cargo
factor so (x-7) (x-1)
i got to there but im not so sure how to get it in the form i want it to be in
proven leaf
first expand the (x-7)(x-1)
tidal cargo
x^2 - 8x + 7
proven leaf
now, do you know how to find the vertex of that parabola? :)
proven leaf
could do that, but there might be an easier way 😅
tidal cargo
hmmm
proven leaf
do you agree that the vertex of the parabola lies halfway between the roots?
proven leaf
so just find the x-value of the parabola by taking the sum of the roots and diving by 2 :) (this is the average)
tidal cargo
ohh i see so the vertex would be at 4, something
proven leaf
yep! now we can just plug 4 into our parabola
this is vertex, and we got the vertex for free! 
no completing the square business
proven leaf
$\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)$ is your friend
ocean sealBOT
MrFancy
tidal cargo
what variable does the f represent?
tidal cargo
ohh i see
okay!
wait so for the answer writing y=(x-1)(x-7) is enough? i dont have to convert it to fit into y-k = f(x-h)?
proven leaf
it want's us to convert it into $y=a(x-h)+k$ I assume
ocean sealBOT
MrFancy
tidal cargo
heres what the answer key says
the factored answer makes sense but i'm not really seeing how i can turn that into the second one
modern rune
Can someone help me with my homework
tidal cargo
.close
red drum
lone heartBOT
red drum
help pls!!
swift tulip
ok well we know that the limber yard pays $4,791.60 per day
those are not their revenue
but instead
what they have to pay
for example if i set up a lemonade stand
i have to pay for the lemons, sugar, water, and whatever tf you put in lemonade
red drum
yes
swift tulip
so you understand the lumber yard pays $47971.60 per day for things like supplies, right?
red drum
yes sir
red drum
i juts know that Cost function is the 4791.60
swift tulip
and then we see that they sell wood per the board foot
we want to assume worst case scenario
like they sell every board for the least possible
otherwise then if you assume you sell, say, $1.37 per board foot, then you might sell less than that and you wouldnt get as much as you planned
swift tulip
planning for worst case scenario will ensure you get at least how much you expected
so now
$1.37 +- 0.27
its between $1.10 and $1.64
worst case scenario, they only sell each board foot for $1.10
now its just division
we want to have revenue of exactly $4791.60 to break even
red drum
right
swift tulip
break even just means that profits = 0
and profits = revenue - losses (cost)
so that means that revenue = losses
good?
red drum
good
swift tulip
so that means that if we sell x boards then we have 1.10x dollars in revenue
and that should equal 4791.60 (our losses) for zero profit
so 1.10x = 4791.60, so just divide
i just broke it down step by step so youd understand
was that good?
swift tulip
ok well go over it again
worst case
the lumber yard seels for only $1.10 per board foot
thats bad
they want to sell their wood for higher prices, right?
swift tulip
that is the minimum price of wood they can sell
well if i interpreted problem correctly
they said the cost is within $0.27 of $1.37
right?
swift tulip
they'll sell the board foot for anything between $1.10 and $1.64
because if a number is within 0.27 of 1.37
then the least it could be would be 1.37 - 0.27
red drum
right
red drum
oh so you just substract it
swift tulip
and we want to pretend the price they sell at is as small as possible in order to guarantee we earn at least how much we expected
yesyes
swift tulip
we just divide
swift tulip
yes
red drum
4356
swift tulip
just use .close to close it now
red drum
u expalin is so easy
swift tulip
no problem
red drum
i love you
swift tulip
thank you
swift tulip
thank you
red drum
.close
swift tulip
bye
lone heartBOT
lone heartBOT
Available help channel!
unique torrent
lone heartBOT
gilded galleon
-30 m/s
unique torrent
It is, but it’s not 30 at 2.5s
It’s close but it’s not
The hard part is that one have to calculate it
Which I, unfortunately, completely forgot how to💀
placid zinc
Similar triangles.
The large triangle has:
- height 45
- base 3
The smaller triangle has
- height ?
- base 0.5
shrewd sky
lone heartBOT
shrewd sky
Wtf
lone heartBOT
Available help channel!
whole lion
i need help
lone heartBOT
i need help
whole lion
i need to give a calculator ready expression for a math problem
ocean sealBOT
@whole lion
whole lion
tried checking answer key, all it did was give me 2 decimal numbers
all i know is that theta is in quadrants 1 AND 3
,tex It's easy to say that $\theta = tan^{-1}(2.5)$, but I can't use that for the 3rd quadrant because the domain of inverse tangent does not extend into there.
ocean sealBOT
@whole lion
ocean sealBOT
@whole lion
whole lion
but i have another question
I need to find the inverse of this function:
,tex $f(x) = x^{3} - 3x$
ocean sealBOT
@whole lion
whole lion
,tex $f(x) = x(x^{2} - 3)$
ocean sealBOT
@whole lion
whole lion
and idk what to do from here
ocean sealBOT
bleak geyser
Easy 
whole lion
wth is this
bronze zodiac
lone heartBOT
bronze zodiac
my head is stucked
at first i thought about looking for potential rational zeros
but i cant find any that works
unless it isnt asking for that
oak turret
there should be a rational zero
sour dove
can confirm I see something you can factor by grouping
fair cobalt
Oh good I thought so.
bronze zodiac
so (2x-3)(x^2-7)
carmine raft
how to i get help
lone heartBOT
how to i get help
lone heartBOT
@carmine raft Has your question been resolved?
carmine raft
useless server
tacit arch
useless server
!volunteers
lone heartBOT
useless server
Helpers are just people volunteering their time to help you. Be polite and patient.
lone heartBOT
@carmine raft Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Why can I not have 0 in f'(x)=4t^3 - 1/4t^(-3/4)?
lone heartBOT
Why can I not have 0 in f'(x)=4t^3 - 1/4t^(-3/4)?
alpine sable
but I can have it in f(x)=t^4-t^(1/4)
remote heron
you mean why is f'(0) not defined but f(0) is?
alpine sable
you mean why is f'(0) not defined but f(0) is?
I don't know what that means
remote heron
i dont know what you mean "have 0 in"
alpine sable
I am asking why the definition is R>=0 for f(x) but it's R>0 for f'(x)
remote heron
well you can rewrite f'(x)
$f'(t) = 4t^3 - \frac14 t^{\sfrac{-3}{4}}$.
this is $f'(t) = 4t^3 - \frac14 \frac{1}{t^{\sfrac34}}$
remote heron
do you see the problem?
alpine sable
do you see the problem?
that you can't divide by 0
alpine sable
wait
remote heron
think $\sqrt x$ is just fine as x -> 0
alpine sable
wasn't x^(m/n) the same as nsqrt(x^m)?
ocean sealBOT
jan Niku
remote heron
wasn't x^(m/n) the same as nsqrt(x^m)?
not sure what property youre thinking of here
alpine sable
not sure what property youre thinking of here
wait one sec
no wait wrong one
sorry
one second
remote heron
it is
remote heron
its also $\sqrt{ \sqrt {x} }$
ocean sealBOT
jan Niku
remote heron
so if you have some intution about $\sqrt x$
ocean sealBOT
jan Niku
remote heron
and how it behaves around 0
remote heron
I mean like
sqrt(0)=0 is just fine
and then everything bigger is good
you get this nice bijective one-to-one function
idk no point on leaning on intuition thats not there
remote heron
so I can put 0 under the sqrt
you can put 0 under the sqrt
if $f(x)=x^{1/4} = \sqrt{\sqrt x}$
ocean sealBOT
jan Niku
remote heron
then $f(0) = 0^{1/4} = \sqrt{\sqrt 0} = \sqrt 0 = 0$
ocean sealBOT
jan Niku
remote heron
well x not 0
alpine sable
well x not 0
ah yeah sorry
ahhh
I get it nonw
because the exponent with f' is negative it is now 1/x
so the issue isn't with the sqrt
it's with the 1/x
tysm 🙏
ocean sealBOT
jan Niku
remote heron
this is an issue anywhere that f shrinks
because as it shrinks, the fraction wil get really really big
shrink meaning to 0
so if you have this and youre curious about some point not working you should check if f is getting really really small near that point
alpine sable
is x getting small a bad thing?
remote heron
in this specific example? it doesnt matter per se
its more an issue of f
like uhh
this is really contrived but
$\frac{1}{\sfrac 1x}$
ocean sealBOT
jan Niku
ocean sealBOT
jan Niku
remote heron
here youll have issues around x=4
alpine sable
I think I understand it
but the tldr
is 0 under : is nono
and the long version is what you described
aka what I hope to have understood
remote heron
power rule can make division by 0 pop out, yea
watch out for negative exponents
tldr
remote heron
np
alpine sable
remote heron
is my cat
remote heron
hes getting screened for lung cancer soon i think
alpine sable
oh
remote heron
send thoughts and prayer
alpine sable
im sorry to hear that
remote heron
its okay 😄 i think the vet is full of shit
alpine sable
but dont worry ive been to radiation screenings before
they sound super dramatic
but they're actually quite peaceful
you just lie down and vrmmmmmmm
alpine sable
then they have a photo of your insides
it's much better than a colonoscopy
that's
yeah
no
remote heron
bwahaha
remote heron
yup
alpine sable
I gotta head to school 😭
remote heron
have a good one
alpine sable
peace
pine valve
lone heartBOT
pine valve
hi so i'm working on this problem and I dont know much, but what I do knkow is how to find the slope
or at least i think you're supposed to find the slope first
forest cobalt
yeah pretty much
pine valve
do you know which point i'm supposed to use since there isn't really an accurate place
forest cobalt
It should be safe to estimate the locations. Look to the left and right of t = 60
there are some points there that nearly touch the grids
easy to read
pine valve
so let's say i find the slope, how do i find the rate of change
forest cobalt
the slope IS the rate of change
the slope gives you the change in temperature over a period of time
pine valve
i tried and it didnt seem to work out
forest cobalt
what did you enter
pine valve
i found two points: (30, 150) & (60, 130)
so slope is = -3/2
forest cobalt
lol no need to apologize
pine valve
.close
wooden pewter
I'm having troubles with this one
lone heartBOT
I'm having troubles with this one
keen wagon
the diagram is very misleading
grand girder
I'm having troubles with this one
The diagonals of a rhombus intersect perpendicularly and centre each other. Does that give you an idea?
lone heartBOT
@wooden pewter Has your question been resolved?
rotund jolt
The odd function y=f(x) increase in (0,+∞),and f(2)=0,find the set that Satisfy f(x)>0
echo socket
Increasing strictly or monotonically?
lone heartBOT
@rotund jolt Has your question been resolved?
rotund jolt
Strictly
rotund jolt
How to I draw full according to question
hardy urchin
f(x) is odd
$f(-x)=-f(x)$
ocean sealBOT
Amir
hardy urchin
How to I draw full according to question
symmetrical origin
shadow sparrow
lone heartBOT
shadow sparrow
I got to this point in the solution, but I forgot how to solve from here to be honest
$1-x^2-y^2-5y^2=0$
ocean sealBOT
Huntifer
shadow sparrow
How would I get rid of the squares? I was thinking square root, but not sure how that would work out
mortal trellis
5y^2 and (5y)^2 are different
shadow sparrow
5y^2 and (5y)^2 are different
Yeah sorry, its the latter.
I ended up reducing down to this
mortal trellis
not sure why you set it equal to 0
shadow sparrow
$-x^2-6y^2=-1$
ocean sealBOT
Huntifer
shadow sparrow
Thats how it says to optimize it
mortal trellis
you are mixing up stuff
shadow sparrow
At least how we learned to do it
mortal trellis
you have to set the derivative equal to 0
shadow sparrow
So you take the sub x and sub y derivative after the substitution and then set that equal to 0, same as your would for a lagrange?
mortal trellis
that said, you can also just read off the maximum. you are subtracting squares. squares are always >=0.
I have to go
lone heartBOT
@shadow sparrow Has your question been resolved?
alpine sable
a
alpine sable
sorry what
keen zenith
If the domain of x^2 is restricted to -infinity to 0 then what would it’s range be?
vale wigeon
If the domain of x^2 is restricted to -infinity to 0 then what would it’s range ...
!occupied
lone heartBOT
If the domain of x^2 is restricted to -infinity to 0 then what would it’s range ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
vale wigeon
(it's a strange kind of occupied, but still, it's got somebody else's name on it.)
vale wigeon
sorry what
you posted in an available help channel, now it got opened in your name.
do you have a question to ask?
if not you can just .close
alpine sable
you posted in an available help channel, now it got opened in your name.
i want a website to practice discrete mathematic questions
well i honestly just wanna know if there is smth like that
alpine sable
ook man
tame tulip
discrete?
alpine sable
yeah
tame tulip
as is discrete random variables? as in statistics?
alpine sable
discrete mathematics as in set theory, proposition
and such
i might wanna check out a book ig
tame tulip
ahh i dunno abt that sorry
lone heartBOT
Available help channel!
alpine sable
How to do this? and what is this method called; https://www.youtube.com/shorts/2kUCPkzNW_U
alpine sable
Just give me the name of the method; and i can learn it in youtube; i forgot how to do this.
vale wigeon
i don't think this method has a name
they're just treating the interest as simple and applying it for half a year
alpine sable
they're just treating the interest as simple and applying it for half a year
umm do you know any way i can learn it? like the cutting part;
like some youtube video
alpine sable
I remember learning this years ago; but truth be told I'm terrible at math's and have completely forgotten all the basics
but if there is some video where they explain how they do it step by step; I'm confident i'll recall and be all good
alpine sable
Yes
vale wigeon
and simplifying fractions / cancelling out common factors etc.
alpine sable
yes
alpine sable
sorry
vale wigeon
anyway like "intro to fractions" "how to multiply fractions" "how to reduce fractions"
look those things up if you want videos
alpine sable
okay, thank you.
tardy stag
this is specifically referred to as "cross-cancelling" sometimes
alpine sable
this is specifically referred to as "cross-cancelling" sometimes
I've started to get an idea on how it works; what exactly what i have to search for to get an example to the one i posted? to calculate an interest.
instead of just this
oh nvm i think it's just whole numbers and fraction multiplied, right?
ocean sealBOT
hayley!
alpine sable
🙏
twilit gull
lone heartBOT
twilit gull
Should I start with $sin(x/100) not equal 0$
ocean sealBOT
Muffins
alpine sable
$\sin\frac{x}{100} \neq 0$
ocean sealBOT
f1dbefdd4de64fb4
mellow grail
Should I start with $sin(x/100) not equal 0$
I think you should start from the outside
twilit gull
The log part right?
twilit gull
Still i would have to face the sin part
mellow grail
Yes, but outside restricts your domain more
timber cobalt
Still i would have to face the sin part
Well sin equals to 0 only in 2 places on the circle so x/100 can't occupy those places
twilit gull
Well sin equals to 0 only in 2 places on the circle so x/100 can't occupy those ...
But the pattern would still repeat
like for multiples of pi
timber cobalt
x is not equal 100 * pi / 2 * N where N is any integer number
twilit gull
x is not equal `100 * pi / 2 * N` where N is any integer number
yess
Wait Im getting same
or is it 100n pi
twilit gull
but sin pi/2=1
timber cobalt
Sorry, pi
timber cobalt
The formula for the area of a cycloid is 3 * pi * r^2.
However I tried to get the formula myself and got a different result.
The cycloid's length is 2 * pi * r, which is equal to the circle's circumference. I assumed the cycloid would follow the circle in the curve's proportions so we could just take all the vertical indivisibles and multiply their width by pi so the formula would be pi^2 * r^2. Where was I wrong?
alpine sable
Have you been taught about when you do the same thing to both sides of an equation the equation stays true?
drifting zenith
Have you been taught about when you do the same thing to both sides of an equati...
no
vale wigeon
can someone help?
!occupied
lone heartBOT
can someone help?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
tardy stag
can someone help?
hi please use a new channel, this one belongs to Telov
drifting zenith
oh ok
vale wigeon
take all the vertical indivisibles and multiply their width by pi
timber cobalt
> take all the vertical indivisibles and multiply their width by pi
<:thonk:4065...
If we take the upper half of a circle, we can say that it consists of infinitely small columns. You get the idea I guess. So I thought if we simply multiplied their width we'd get the cycloid's area. The cycloid's length relates to the circle's length as Pi so I multiplied by Pi.
Are you familiar with the method of indivisibles (Cavalieri's principle)?
vale wigeon
this sounds like some kind of screwed up way of talking about an integral
timber cobalt
Well it predates integral
timber cobalt
Well it isn't but I thought it would be equal to one
timber cobalt
What did you use to create that?
vale wigeon
desmos
timber cobalt
Nice
Okay I see they are not equal but it would be nice to understand how exactly they become different...
vale wigeon
btw 2pi is only the distance between the cycloid's endpoints
or at least of one arch of it
the length of the cycloid itself is actually 8
timber cobalt
Circumference you mean
vale wigeon
the cycloid is a curve
if you want to call its length a circumference i can't stop you but i would not use that term
timber cobalt
I mean we use circumference when talking about circles but they are curves too
timber cobalt
Right
vale wigeon
"circumference" is reserved specifically for circles
timber cobalt
So I would be right if we talked about a stretched circle
vale wigeon
area-wise?
timber cobalt
How did you set up the formula for it?
vale wigeon
yeah sure you would.
vale wigeon
How did you set up the formula for it?
parametric equations
x = t - sin(t)
y = 1 - cos(t)
timber cobalt
What is t
timber cobalt
So it's like x = f1(t) and y = f2(t) right?
vale wigeon
if you wanna give them names like that, sure
timber cobalt
Desmos is super cool
And how did you generate a cycloid?
What equations did you use?
vale wigeon
??
do you mean how i entered it into desmos or how i determined the equations to be the ones i wrote
timber cobalt
Determined